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About Alon Mandes
Expertise
Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience
1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

You are here: Experts > Teens > Homework/Study Tips > Calculus > Integration

Calculus - Integration

Expert: Alon Mandes - 7/10/2009

Question
the constant a is such that integration of (xe^.5x) with limits a to 0 equal to 6.Show that a satisfies the equation x=2+e^(-.5x). Thanks

Answer
The integral of xe^(x/2) is 2(x-2)e^(x/2). This can be easily shown
via "Integration By Parts" method :
Let's set x=v & e^(x/2)=du . Thus :
INT of xe^(x/2) = 2xe^(x/2) - INT of 2e^(x/2)
= 2xe^(x/2)-4e^(x/2)
= 2(x-2)e^(x/2).
So,
INT from 0 to a yields : 2(a-2)e^(a/2) + 4 .
Hence, our equation for a will become :
6=2(a-2)e^(a/2) + 4
2=2(a-2)e^(a/2)
a-2=e^(-a/2)
a=2+e^(-a/2) .

Alon.

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